A129412 Numbers k such that mean of 7 consecutive squares starting with k^2 is prime.

0, 2, 4, 10, 12, 14, 24, 30, 32, 34, 42, 44, 54, 62, 64, 70, 82, 84, 92, 94, 100, 112, 114, 122, 132, 134, 144, 152, 160, 164, 174, 180, 190, 200, 204, 212, 214, 230, 232, 240, 242, 250, 252, 262, 264, 272, 274, 284, 290, 300, 304, 310, 314, 344, 354, 370, 372

Offset: 1

Author

Zak Seidov, Apr 14 2007

Keywords

• nonn
• easy

Comments

Sum of 7 consecutive squares starting with k^2 is equal to 7*(13 + 6*k + k^2) and mean is (13 + 6*k + k^2) = (k+3)^2+4. Hence a(n) = A007591(n+1)-3.

Examples

			(0^2+...+6^2)/7=13 prime, (2^2+...+8^2)/7=29 prime, (4^2+...+10^2)/7=53 prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005473, A056899, A067201, A007591, A129389, A098062.

Programs

Mathematica

Select[Range[0,400],PrimeQ[Mean[Range[#,#+6]^2]]&]  (* Harvey P. Dale, Apr 23 2011 *)

PARI

is(n)=isprime(n^2+6*n+13) \\ Charles R Greathouse IV, Jun 13 2017